In this paper we investigate a system of coupled inequalities consisting of a variational–hemivariational inequality and a quasi-hemivariational inequality on Banach spaces. The approach is topological, and a wide variety of existence results is established for both bounded and unbounded constraint sets in real reflexive Banach spaces. Applications to Contact Mechanics are provided in the last section of the paper. More precisely, we consider a contact model with (possibly) multivalued constitutive law whose variational formulation leads to a coupled system of inequalities. The weak solvability of the problem is proved via employing the theoretical results obtained in the previous section. The novelty of our approach comes from the fact that we consider two potential contact zones and the variational formulation allows us to determine simultaneously the displacement field and the Cauchy stress tensor.

中文翻译：

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具有非线性耦合的变分-半变分不等式系统的存在性结果

在本文中，我们研究了由巴纳赫空间上的变分-半变分不等式和拟半变分不等式组成的耦合不等式系统。该方法是拓扑的，并且为实自反巴纳赫空间中的有界和无界约束集建立了各种各样的存在结果。本文的最后一部分提供了接触力学的应用。更准确地说，我们考虑具有（可能）多值本构律的接触模型，其变分公式导致不等式的耦合系统。利用上一节获得的理论结果证明了该问题的弱可解性。我们方法的新颖之处在于我们考虑了两个潜在的接触区域，并且变分公式使我们能够同时确定位移场和柯西应力张量。